spin-orbit coupling induced magneto-resistance effects in ferromagnetic semiconductor structures:...
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Spin-orbit coupling induced magneto-resistance effects in ferromagneticsemiconductor structures: TAMR, CBAMR, AMR
Tomas Jungwirth
University of Nottingham Bryan Gallagher, Richard Campion, Kevin Edmonds, Andrew Rushforth, Tom Foxon, et al.
University & Hitachi Cambridge Jorg Wunderlich, Andrew Irvine, Elisa de Ranieri,
Byonguk Park, et al.
Institute of Physics ASCRKarel Výborný, Jan Zemen, Jan Mašek, Vít Novák, Kamil Olejník, Ludvík Smrčka,
Jan Kučera, Nataliya Goncharuk, et al.
University of Texas Allan MaDonald, Maxim Trushin,et al.
Texas A&MJairo Sinova, et al.
Wuerzburg University Charles. Gould, Laurens Molenkamp, et al.
Experimental observation of (ohmic) AMR
Lord Kelvin 1857
Inductive read elements Magnetoresistive read elements
AMR sensors: dawn of spintronics
Now often replaced by GMR or TMR but still extensively used in e.g. automotive industry
magnetization
current
1980’s-1990’s
ss sd
sdss
itinerant 4s:no exch.-split
no SO
localized 3d:exch. split
SO coupled
Theory of AMR: current response to magnetization via spin-orbit coupling
Model for transition metal FMs:
Banhart&Ebert EPL‘95
Miscroscopic theory: relativistic LDA & Kubo formula
theory
experiment
?
Smit 1951
FeNi
x=0.07%
1%
2.5%
7%
Jungwirth et al. PRB ’07
<<0.1% Mn
~0.1% Mn
>1.5% Mn~
MnGa acceptor: electrical conduction similar to conventional p-doped GaAs
Renewed research interest in AMR due to FS like (Ga,Mn)As
metallic
insulating
Ohno. Science ’98
(Ga,Mn)As
(Ga,Mn)As
Ni
d/d
T~c
v
Tc
h+
h+
Mn moment:Ferromagnetism reminiscent of conventional metal band FMs (Fe, Co, Ni,..)
Novak et al. PRL ’08
Renewed research interest in AMR due to FS like (Ga,Mn)As
>1% Mn~
ferromagneticTc
Baxter et al. PRB ’02, Jungwirth et al. APL’02, ‘03
Renewed research interest in AMR due to FS like (Ga,Mn)As
AMR’s of order ~1-10%: - routine characterization tool- semi-quantitatively described assuming scattering of valence-band holes
SET
Resistor
Complexity of the device design
Magnitude, control, and tuneability of MR
DOS
Simple direct link between band structure and transport
Tunneling DOS TAMR
Chemical potential CBAMR
Scattering lifetimes ohmic AMR
heterostructures
bulk
micro-structures
MTJ
Magnetic anisotropies in (Ga,Mn)As valence band
Dietl et al. PRB ’01, Abolfath et al. PRB ‘01
exchange-split HH bands and LH bands in (Ga,Mn)As:
anisotropic due to crystal, SO coupling and FM exchange field
M
j=3/2
HH
HH
HH
degenerate HH bands and LH bands in GaAs:
anisotropic surface and spin-texture due to crystal and SO coupling in As(Ga) p-orbitals
HH & LH Fermi surfaces
TAMR: spectroscopy of tunneling DOS anisotropy
M
M
Selectivity tuned by choice of barrier, counter-electrode, or external fields
GaMnAs
barrier
electrode
Vbias
Binpl
Giddings et al. PRL ’04
k - resolved tunneling DOS
TAMR: spectroscopy of tunneling DOS anisotropy
M
M
GaMnAs
AlOx
Au
Non-selective barrier and counter-electrode only a few % TAMR
Gould et al. PRL ’04
TAMR: spectroscopy of tunneling DOS anisotropy
M
M
Giraud et al. APL ’05, Sankowski et al. PRB’07, Ciorga et al.NJP’07,Jerng JKPS ‘09
Giraud et al. Spintech ’09
n-GaAs:Si
p-(Ga,Mn)As
Very selective p-n Zener diode MTJs
Binpl
TAMR: spectroscopy of tunneling DOS anisotropy
M
M
Extra-momentum due to Lorentz force during tunneling
Giraud et al. Spintech ’09
Binpl
n-GaAs:Si
p-(Ga,Mn)As
Very selective p-n Zener diode MTJs
GM
MGG
C
C
e
MV
MVVCQC
QQU
)(&
)]([&2
)(0
20
electric && magneticmagnetic
control of CB oscillations
Source Drain
GateVG
VDQ
CBAMR: M-dependent electro-chemical potentials in a FM SET
Wunderlich et al. PRL ’06
[110]
[100]
[110][010]
M
Huge MRs controlled by low-gate-voltage: likely the most sensitive spintronic transistors to date
Wunderlich et al. PRL ’06
Schlapps et al. arXiv:0904.3225
SET
Resistor
Chemical potential CBAMR
Tunneling DOS TAMR
Scattering lifetimes AMR
DOS
Simple direct link between band structure and transport
MTJ
Simplicity of the microscopic picture of AMR in (Ga,Mn)As
- -MnGa MnGa
M
CBAMR,TAMR:SO & FM polarized bands
ohmic AMR: main impurities – FM polarized random MnGa can consider bands with SO coupling only
SET
MTJ
Resistor
AMR: M vs current (non-crystalline) term can be separated and dominates in (Ga,Mn)As
Simplicity of the microscopic physical picture in (Ga,Mn)As
TAMR: current direction is cryst. distinct inseparable M vs current term
CBAMR: only el.-chem potentials no M vs current term M
cryst. axis
current
M
cryst. axis
current
M
cryst. axis
current
SET
MTJ
Resistor
KL Hamiltonian in spherical approximation
Heavy holes
Electro-magnetic impurity potential of MnGa acceptor
3/ˆ1̂ˆ1̂~ js MM eeVimp
Rushforth PRL’07, Trushin et al. arXiv:0904.3785, Vyborny et al. arXiv:0906.3151
current
MGa
Key mechanism for AMR in (Ga,Mn)As:
FM impurities & SO carriers in non-cryst.-like spherical bands
Pure magnetic MnGa impiruties: positive AMR,
current
0|~|ˆ| xj0|~|ˆ| xj
0|~|ˆ| yj
0|~|ˆ| xj
jMˆ~ eVimp
- -
0|~|ˆ| yj
Backward-scattering matrix elements
)()||( IMIM
current
0||~|/ˆ1̂| jjx
0||~|/ˆ1̂| jjx
0|~|/ˆ1̂| jjy
0|~|/ˆ1̂| jjx
jeVimp /ˆ1̂~ jM
- -
Backward-scattering matrix elements
Electro-magnetic MnGa impiruties: negative AMR, )()||( IMIM
AMR= -202-1
244-2 4+1
p [1021 cm-3]
AM
R
current
- -
3/ˆ1̂~ jM eVimp
~ screened Coulomb potential
all scatt.backward scatt.
Electro-magnetic MnGa impiruties: negative AMR, )()||( IMIM
current
- -
AMR= -202-1
244-2 4+1
p [1021 cm-3]
AM
R
~ screened Coulomb potential
all scatt.backward scatt.
Electro-magnetic MnGa impiruties: negative AMR, )()||( IMIM
3/ˆ1̂~ jM eVimp
Straightforward intuition for AMR in Rashba and Dresselhaus 2DEGs
& exact analytical solutions to full integral Boltzmann equation SO-coupled 2DEGs are ideal testbed to study AMR
Trushin et al. arXiv:0904.3785
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